JEE MATHEMATICS MCQ: STRAIGHT LINES

1 Medium

1 of 1

Application +4 | -1

The straight line

y=m x+c

cuts the circle

x^2+y^2=a^2

at the real points if

View answer and explanation

Correct option: C

\sqrt{a^2\left(1+m^2\right)} \geq|c|

Option C,

\sqrt{{a^2\left(1+m^2\right)}} \geq|c|

, is correct because it represents the condition where the distance from the center of the circle to the line is less than or equal to the radius, ensuring real intersection points.

More Questions from STRAIGHT LINES

Practice All Chapter MCQs →

If the three lines

x-3 y=p, a x+2 y=q

and

a x+y=r

form a right-angled triangle then :
The orthocentre of the triangle whose vertices are

\left\{ {a{t_1}{t_2},\;a\left( {{t_1} + {t_2})\} ,\{ a{t_2}{t_3},a({t_2} + {t_3}} \right)} \right\},\;\left\{ {a{t_3}{t_1},\;a\left( {{t_3} + {t_1}} \right)} \right\}

is
The distance between the parallel lines

y = 2\;x + 4

and

6x = 3y + 5

is The distance between the pair of lines given by

{x^2} + {y^2} + 2xy - 8ax - 8ay - 9{a^2} = 0

is Find the image of the point

(3,8)

with respect of the line

x+3 y=7

assuming the line to be plane mirror: The centroid of the triangle whose three sides are given by the combined equation

\left( {{x^2} + 7xy + 2{y^2}} \right)\left( {y - 1} \right) = 0